In this two-step process, both the basis and coefficients are updated. Extensions to schemes with high order spatial and temporal discretizations and to high dimensional problems, are developed in [1]}. The low rank approach [1]} is built upon the classical high order methods for conservation laws and kinetic equations, yet it optimizes the computational efficiency by dynamically building low rank global basis and updating the corresponding coefficients via an SVD truncation procedure. While the SVD truncation significantly reduces the computational storage and cost complexity, it also destroys the desired conservation property.
